Bernd A. Kniehl

Δr beyond one loop

Abstract We study the effect of two-loop contributions on the radiative corrections to the muon lifetime in the standard electroweak model. O( αα s ) contributions are fully included. We also incorporate all dominant O( α 2 ) corrections and identify those logarithms which can be resummed. We present an explicit expression for Δr which fully exploits our present knowledge of contributions beyond one loop. The phenomenological implications are presented in terms of the m t − M w relation. The known higher-order effects are found to be equivalent to variations in the W-boson mass of order 100 MeV i.e. the anticipated experimental error, and to variations in the Higgs-boson mass over the range 50 GeV−1 TeV, i.e. the range bracketed by the current experimental limit and the unitary bound.

Dispersion relations for vacuum polarization functions in electroweak physics

Abstract We propose a class of once-subtracted dispersion relations for the vacuum-polarization functions of massive fermions, in which the subtraction constants are determined explicitly from Ward identities. We show that in perturbation theory to O(α) and O(ααs) this approach, the alternative dispersion relations proposed by Chang, Gaemers and van Neerven, and dimensional regularization all give the same contributions to electroweak observables such as Δϱ and Δr. The threshold behaviours of the subtraction integrands are, however, very different and the two dispersion methods are expected to lead to significantly variant estimates of contributionsarising from non-perturbative tt threshold effects.

Elastic ep scattering and the Weizsäcker-Williams approximation

Abstract We derive a general expression for the total cross section of the production of an arbitrary multi-particle state, X, in elastic ep scattering, ep→Xp, which depends on two invariants associated with the subprocess eγ ∗ →X . From this we extract a modified Weizsacker-Williams distribution appropriate for elastic ep scattering. We apply these results to study associated νW production at future ep colliders.

Radiative corrections for H → ZZ in the standard model

Abstract An analytic expression for the one-loop radiative corrections to the HZZ vertex is derived within the minimal standard model of electroweak interactions. The influence of a fourth generation of heavy fermions is investigated. Approximation formulae are presented for the contribution from light fermions and for the case that the Higgs boson is heavy as compared to the weak vector bosons. These results are used to study the Higgs-boson decay mode H → ZZ in the modified on-mass-shell scheme. The partial decay width may be enhanced by up to 15%, if the masses oof both the Higgs boson and the top quark assume values close to their theoretical upper bounds.

Radiative corrections for H → ƒ ƒ (γ) in the standard model

Abstract The partial widths of the fermionic Higgs-boson decays are calculated in the one-loop approximation of the minimal standard model of electroweak interactions. The soft-photon bremsstrahlung is resummed by means of Yennie-Frautschi-Suura exponentiation and the hard-photon spectrum is integrated analytically for a variable maximum photon energy. A general expression for the weak corrections in the modified on-mass-shell scheme is presented. For the charged-lepton and light-quark modes the formulae may be greatly simplified by neglecting the masses of all fermions, except for the top quark. For the b b and t t channels individual approximation formulae are derived assuming that the Higgs boson and the top quark are heavy as compared to the weak gauge bosons. Below the t t production threshold the electroweak corrections are generally at the few-percent level but for a 1 TeV Higgs boson they may become as large as 15%.

Radiative corrections for H→W+W−(γ) in the standard model

Abstract The HW + W − three-point function with all external particles being off-mass-shell is calculated in the one-loop approximation of the minimal standard model of electroweak interactions. The effect of radiative corrections on the Higgs-boson decay mode H→W + W − ( γ ) is examined. The soft-photon bremsstrahlung is resummed using Yennie-Frautschi-Suura exponentiation and the hard-photon spectrum is integrated analytically. The impact of a fourth generation of heavy fermions is investigated. Approximation formulae are presented for the light-fermion contribution and for the case that the Higgs boson is heavy as compared to the weak vector bosons. In the modified on-mass-shell scheme the partial decay width may be enhanced by up to 15% if the masses of both the Higgs boson and the top quark assume values close to their theoretical upper bounds.

Comparative analysis of three methods to evaluate vacuum-polarization functions

Abstract The O (αα S ) contributions to the H 0 a l + l − decay width are studied on the basis of two different classes of dispersion relations for the vacuum-polarization functions of vector bosons, and compared with the results obtained using dimensional regularization. It is found that the latter agrees with one of the two approaches, thus providing explicit support to this formulation. This result also gives additional support to recent evaluations of the threshold contributions to basic corrections of the electroweak theory, as such analyses are based on the same dispersion relations.

Two-loop QED vertex correction from virtual heavy fermions

Abstract The O(α2) contribution of a virtual massive fermion to the electromagnetic vertex of a light fermion is calculated in perturbative QED for arbitrary external momentum transfer s. Besides the exact analytic result also the small-s and high-s expansions are presented. Virtual fermions with masses m≫ |s| decouple from the effective interaction of light fermions and photons.

Virtual top effects on low mass Higgs interactions at next-to-leading order in QCD

We present the next-to-leading-order QCD corrections of O(αs2GFMt2) to the low-MH effective l+l− H, W+W− H, and ZZH interaction Lagrangians in the high-Mt limit. In the on-shell scheme formulated with GF, the O(αs2GFMt2) corrections support the O(αsGFMt2) ones and further increase the screening of the O(GFMt2) terms. The coefficients of (αsπ)2 range from −6.847 to −16.201, being in line with the value −14.594 recently found for Δϱ. All four QCD expansions converge considerably more rapidly, if they are written with μt = mt(μt), where mt(μ) is the MS mass, rather than the pole mass, Mt.

The Higgs boson decay H→Zgg☆

Abstract The decay mode H→Zgg is investigated using analytic results for the HZgg vertex in the minimal standard model. It is compared to the major decay channels of the Higgs boson in the window M W M H M W armand B (H→Zgg) −6 is found for the branching ratio.